Imagine a material that has an arbitrarily high specific heat. How well would it work as an energy storage system?

The biggest advantages I can think of it that its energy density would be huge and that safety would not be a particularly big issue, assuming that it is a chemically stable substance. The biggest disadvantages I can think of is that extracting energy from it would take a long time and it would be a pain to recharge. Overall, I think that it would work quite well as a Mars rover's energy source and hooking it up to the electrical grid would be next to useless.

Hooking it up to the power grid would be the most useful thing, since the cost of electricity varies by day and night. Locally: the off peak rate for power is about 30% of the peak rate, so an arbitrarily large ability to store energy is a pretty big deal.

Referring to the Mars rover, you're likely thinking of using this as a battery. The chemical potential of a battery is huge on scales of thermal potential. Also the square cube law works against this working in a rover, because it's too small to have something that's stably at another temperature.

The boring truth is that water is close to the highest possible specific heat for any chemical.

Undiscovered /researched chemicals are larger and have degrees of freedom spent on locking their pieces together.

Ammonia is a little better (1.12 c/g), but much more expensive.

Helium is better yet (1.24 c/g), but it's a gas, and a dense storage is really more storing pressure than thermal energy.

Diatomic hydrogen is much better (3.42 c/g), but the gas problem is worse, and now it's chemical active.

Monatomic hydrogen is presumably better, but it only exists at high temperatures and is highly chemically interactive.

Plasma hydrogen would (I think) about twice as good, but more problems. Including the fact that the plasma is glowing thousands of times brighter than the sun's surface.

My unqualified calculations would give neutrinos capacity of about 5 billion times better than water, but they're basically impossible to store; and if you did store them you would have pressure issues much worse than any of the above.

I did a little paper on non-fossil fuel energy sources for school and the more common problem across the board was that they could not change electrical output on demand. Large amounts of electricity cannot be stored efficiently, so the more electricity that you produce than is needed, the less efficient your power plant is. Power demand fluctuations are measured over the course of 5 minutes by the EPA. In comparison, it can takes days for a nuclear power plant to change its output. If transfer of thermal energy is proportion to the difference of temperature, it would still face this the problem because its temperature cannot change quickly enough to match the change in demands.

Actually, the Mars rovers are powered by the heat generated from radioactive materials as they decay. This battery would basically be a reverse heat sink and the thinner the blades of a heat sink are the more effective it is. I get the feeling that NASA would be able to make paper thin wafers considering they make telescope lenses with a tolerance measured in picometers.

That source gives the specific heat of common materials; it says nothing about exotic or hypothetical materials.

P.S. The idea of molten salt being a thing that exists makes me really happy for some reason.

By "exotic or hypothetical materials" do you mean stuff made out of atoms or not?

We can't take pieces and make a whole with a higher specific heat than then sum of it's parts. When we assemble atoms in a new way (or an old way for that matter) we decrease the entropy because the fact that any assemblage is an ordering, which reduces degrees of freedom for thermal energy.

The thing about recursion problems is that they tend to contain other recursion problems.

The short answer is "we don't know, but we expect it to be complicated"

As for the complexity: A proton consists of two up quarks (2.4 MeV each) and a down quark (4.8 MeV), which combine to form a mass of 938.2 MeV. If you don't know how to get the third number from the first two, you're not alone. Higher energy states have those complications in new combinations that we've see less often (or never). So we don't really know the available energy states, or their patterns of transition.

Also, the specific heat is also likely to rise with temperature. At very high temperatures (at quark-gluon plasma starts forming at about 2 trillion kelvin) fermions start contracting and hence the number of fermions (and as such the entropy) that can fit in that space goes up.

The thing about recursion problems is that they tend to contain other recursion problems.

Quizatzhaderac wrote:The short answer is "we don't know, but we expect it to be complicated"

That is my favorite answer.

As for the complexity: A proton consists of two up quarks (2.4 MeV each) and a down quark (4.8 MeV), which combine to form a mass of 938.2 MeV. If you don't know how to get the third number from the first two, you're not alone.

E=mc2 can be rewritten as m=E/c2, so as the amount of energy in a system increases so does its mass. So much energy is needed to bind the quarks together that the mass of the system as a whole is huge, relatively speaking (pun unintended). I have no idea why we get the exact value of 938.2 MeV, but I am fairly certain that this is the mechanism that is currently credited for it.

Also, the specific heat is also likely to rise with temperature. At very high temperatures (at quark-gluon plasma starts forming at about 2 trillion kelvin) fermions start contracting and hence the number of fermions (and as such the entropy) that can fit in that space goes up.

On the other hand, bosons can contract at very low temperatures. Maybe a graph of temperature vs. specific heat would look like a parabola, with very high ends and a low middle.

jewish_scientist wrote: I have no idea why we get the exact value of 938.2 MeV.

So then what's the total invariant energy if we add a valance quark and antiquark? If we add three more valence quarks? If we add a quanta of orbital angular momentum? What's the additional change of energy after an arbitrarily large number of those additions has already happened?

We need the answer of that last question to tell us what the entropy of the quark-gluon plasma is.

Also that number (938.2 MeV) can't be reached with linear equations, or even (AFAIK) closed form mathematics of any kind.

On the other hand, bosons can contract at very low temperatures

I think you might be think of a Bose-Einstein condensate or something different than I was referring to.

All particles have a Compton wavelength. As the particles become more energetic this wavelength decreases. For mass-less particles doubling the temperature from 3 to 6 K halves the wavelength. For massive particles, 3 to 6 K is a negligible difference. A difference of (say) 2 to 2.1 Tk isn't negligible.

Fermions (such as quarks) obey the Pauli exclusion principle, which means the Compton wavelengths limit how many of them can fit into a given volume.

The thing about recursion problems is that they tend to contain other recursion problems.